A new local stochastic method for predicting data with spatial heterogeneity

Abstract

Spatial data (e.g., phytopathogenic data) do not always meet assumptions such as stationarity, isotropy and Gaussian distribution, thereby requiring complex spatial methods and models. Some deterministic assumption-free methods such as the inverse distance weighting can also be applied to predict spatial data, but their output is limited for graphical solutions (mapping). We adapted a computer-based prediction method called Circular Variable Radius Moving Window (CVRMW) that is based on two others: moving window kriging (MWK) and inverse squared-distance weighting (ISDW). The algorithm is developed to meet an objective function that minimizes the index of variation of the spatial observations inside the moving window. A code in R language is presented and thoroughly described. The outputs include the range of the spatial dependence as the radius calculated at every target location and the standard error of the predicted values, mapped to provide a useful tool for spatial exploratory analysis. The method does not make any assumptions about the spatial process, and it is an alternative for dealing with spatial heterogeneity.